Finding the height of an irregular cylinder?
By Emma Terry •
I need to find the height of an irregular cylinder. Its difficult due to both diameters being different.
Here are the Details
Capacity: 250 Ml Bottom Diameter: 4.8 cm Top Diameter 8 cm
Please help.
$\endgroup$ 22 Answers
$\begingroup$So you are given a truncated cone with $r_1 = 0.048 \text{ m}$, $r_2 = 0.08 \text{ m}$, and volume $V = 0.00025 \text{ m}^3$.
$$ V = \frac{1}{3} \pi h (r_1^2 + r_1 r_2 + r_2^2) $$ So you can plug in your values and solve for $h$ where $$ h = \frac{3 V}{\pi (r_1^2 + r_1 r_2 + r_2^2)} = 0.0190 \text{ m} = 1.9 \text{ cm}$$
$\endgroup$ 3 $\begingroup$Are you describing a conical frustrum? It is a cone with a cone cut off, similar to a trapezoid? If the height is $h$ and the radii are $r_1,r_2$, $$V=\frac 13\pi h(r_1^2+r_1r_2+r_2^2)$$
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